搜索算法指南 (Searching Algorithm Guide)

Prior to this article, I have written about Binary Search. Check it out if you haven’t seen it. In this article, we will be discussing Interpolation Search, which is an improvement of Binary Search when the values in the sorted array are uniformly distributed.

在本文之前，我已经撰写了有关Binary Search的文章 。 如果您没有看过，请检查一下。 在本文中，我们将讨论插值搜索，它是对已排序数组中的值进行均匀分布时二进制搜索的一种改进。

You might recall that Binary Search is already running in O(log n) time complexity. Can there be any other methods that perform even better? Ummm… partly yes. We will dive into it shortly.

您可能还记得二进制搜索已经以O(log n)时间复杂度运行。 还能有其他方法表现更好吗？ 嗯...部分是。 我们将在短期内深入探讨。

什么是插值搜索？ (What is Interpolation Search?)

Interpolation Search is another efficient searching technique. This method can outrun binary search in cases where the elements of the array are uniformly distributed. Interpolation Search estimates the position of the key value in the array. This can be achieved by taking into account the smallest and the largest element in the array and the length of the array.

插值搜索是另一种有效的搜索技术。 在数组元素均匀分布的情况下，此方法可以胜过二进制搜索。 插值搜索估计键值在数组中的位置。 这可以通过考虑数组中最小和最大的元素以及数组的长度来实现。

It is based on the thinking that if the key value is larger (closer to the largest element), it’s position is likely located to the end of the array. The same thing goes for a key with a smaller value.

基于以下想法：如果键值较大(更靠近最大元素)，则其位置可能位于数组的末尾。 具有较小值的键也是如此。

它是如何工作的？ (How Does it Work?)

There are the 6 main steps in doing Interpolation Search, which are:

进行插值搜索有6个主要步骤，它们是：

1. Estimates the middle position for the array and compares this element to the desired key.
   估计数组的中间位置，并将此元素与所需键进行比较。
2. If the key matches the middle element, return the middle location.
   如果键与中间元素匹配，则返回中间位置。
3. If the key is smaller than the middle element, then the key can only lie in the left subarray. Focus on the left subarray
   如果键小于中间元素，则键只能位于左子数组中。 专注于左侧子数组
4. Else, we move our focus only to the right subarray.
   否则，我们仅将焦点移到正确的子数组上。
5. Repeat steps 1, 2, 3, and 4 until the desired key is found or every subarray has been checked.
   重复步骤1、2、3和4，直到找到所需的键或已检查每个子数组。
6. If there is no match in the array, return -1
   如果数组中没有匹配项，则返回-1

插值搜索示例 (Interpolation Search Example)

As usual, the pseudo-code will be provided first before we move to the implementation in different programming languages.

与往常一样，在我们使用不同的编程语言来实现之前，将首先提供伪代码。

Interpolation Search Pseudo-Code

插值搜索伪代码

Now, we will move on to the real code for 3 different languages, Python, C, and JavaScript.

现在，我们将继续使用3种不同语言(Python，C和JavaScript)的真实代码。

Interpolation Search Code in Python

Python中的插值搜索代码

Interpolation Search Code in C

C语言中的插补搜索代码

Interpolation Search Code in JavaScript

JavaScript中的插值搜索代码

插值搜索的时间复杂度 (Time Complexity of Interpolation Search)

In smaller arrays, Interpolation Search is slower than Binary Search. The reason behind this is Interpolation Search requires more computations. However, larger arrays and the ones that are uniformly distributed are Interpolation Search’s forte. The growth rate of Interpolation Search time complexity is smaller compared to Binary Search.

在较小的数组中，插值搜索比二进制搜索慢。 其背后的原因是插值搜索需要更多的计算。 但是，较大的数组和均匀分布的数组是插值搜索的强项。 与二值搜索相比，插值搜索时间复杂度的增长率较小。

The best case for Interpolation Search happens when the middle (our approximation) is the desired key. This makes the best case time complexity is O(1). In the worst-case scenario, we will need to traverse all of the elements in the array, resulting in the O(n) time complexity. The good news is for the average case, the time complexity is as small as O(log log n).

当中间(我们的近似值)是所需的关键点时，就会发生插值搜索的最佳情况。 最好的情况是时间复杂度为O(1)。 在最坏的情况下，我们将需要遍历数组中的所有元素，从而导致O(n)时间复杂度。 好消息是对于一般情况，时间复杂度小至O(log log n)。

结论 (Conclusion)

Summing up, learning how to apply Interpolation Search will enrich your knowledge not only about algorithms but also as a programmer. Undoubtedly, it will have a place in your programming toolkit. However, it should always be remembered:

总结一下，学习如何应用插值搜索不仅可以丰富您的算法知识，还可以作为一名程序员。 毫无疑问，它将在您的编程工具包中占有一席之地。 但是，应始终记住：

1. Similar to Binary Search, Interpolation Search only works in sorted arrays.
   与二进制搜索类似，插值搜索仅适用于排序数组。
2. You need to have direct access to the elements of the array.
   您需要直接访问数组的元素。

There is no easy way to become an expert programmer, the only available path is by persistently learning about the key concepts one by one. So, if I can understand these concepts, so can you.

成为专家程序员没有简单的方法，唯一可行的途径是持续不断地逐一学习关键概念。 因此，如果我能理解这些概念，那么您也可以。

“The secret to getting ahead is getting started.”

“取得成功的秘诀就是开始。”

— Mark Twain

—马克·吐温

Let’s go to the top together!

让我们一起去顶吧！

Regards,

问候，

Radian Krisno

拉迪安·克里斯诺(Radian Krisno)